The General Form of the equation of a circle is x^2 + y^2 + 2gx +2fy + c = 0. Find the centre of the circle and the radius of the circle in terms of g f and c.

Given a circle in the general form you can complete the square to change it into the standard form.x² + 2gx + y² +2fy +c = 0 (1). General form of an equation which has the completing the square method applied to it is (x+d)² + e. By completing the square we want the expression to look like (x+d)² + e + (y + j)² + k + c = 0, where d e j and k are all constants.Expanding this expression: x² +2dx + d² + e + y² + 2jy + j² + k +c = 0 (2). Comparing equatons (1) and (2) d=g, f=j, d² + e = j² + k =0. Therefore e = - g² and k = -f². Equation (1) can be rewritten as (x+g)² + - g² + (y + f)² + -f² + c = 0. Rearranging: (x+g)² + (y + f)² = g² + f²- c. The equation of a circle with centre (a, b) and radius r is (x - a)² + (y - b)² = r². Therefore a = -g, b= -f, r = √(g² + f²- c).Answer: Centre is (-g, -f), Radius is r = √(g² + f²- c)